@Buttmonki, this confusion makes sense. One set of instructions says turn skis with legs while keeping the pelvis and upper body not turning, and another set of instructions says allow the pelvis and upper body to turn with the skis. I used to wonder about this too.
The general rule is the shorter the turn radius, the more the separation. Meaning, for your shortest turns, when you are skiing inside a very narrow corridor, straight down the fall line, keep the upper body (pelvis and shoulders) facing straight downhill while the skis and legs turn beneath. The pivot point is the top of the femur where it connects to the pelvis. AKA "hip joint." Your skis will be skidding, not carving. Pivot slips are an excellent drill, taking this to the extreme. (It sounds like Jilly uses the waist as the pivot point... here in PSIA land we use the top of the femur as the pivot point for the separation, and keep the pelvis and shoulders pointing together in the same direction.)
For your longest radius turns, where you move left-right a long way across the hill with each turn, and head downhill for a looong time in the middle of the turn, there's no need to separate upper body from legs. Just face the way you are heading. These turns can be carved, with no skidding at all, if you are interested or willing in going at crazy speeds. You'll still need to angulate for the skis to grip, and this requires a bit of separation (counter), but it's only a little and accompanies the angulation to make it easier, causing less pinch in the waist area.
For all the turns in between, which are most of our turns, you have a choice. If you are attempting to carve, reduce the separation. Why? Because a twisted body wants to untwist. When the skis flatten between turns, that body, if allowed to do its thing, will untwist and rotate the skis across the snow. There goes your carved turn, destroyed by ski rotation across the snow surface.
If you want to use friction to control your speed with skidded turns, then by all means use separation. These turns will be on the shorter end of the spectrum (turn radius wise), and maybe on steeper or icier terrain. They will be "short radius turns" but not super short.
Just remember, entering a turn with separation, meaning the pelvis and shoulders stay pointing downhill at the end of the old turn, while the skis are traveling across the hill, encourages and/or supports a skidded turn, and is intentionally used for shorter radius turns for that reason. Most good turns are skidded, in a good way.
None of this means don't use angulation with a bit of separation to direct pressure to the outside ski as the turn develops. I don't think the necessary bit of separation that allows angulation is what your instructor is trying to get you to remove.
What your instructor is definitely NOT saying is to sling your shoulders around to get the turns started. This is a beginner's mistake. It works wonderfully, especially if the skier is in the back seat. But using the upper body to turn the skis, instead of starting with the feet and legs to get the skis to do their thing, is a very bad idea. Beginners discover this and use it, thinking it's a good idea. Nope, start turns with the feet and legs.
Well, there are special circumstances when using upper body rotation to start at urn comes in handy, but not as a general habit.
What I'm thinking is that your instructor may be trying to get you to allow the skis to tip and grip earlier in the turn, rather than being rotated by your unwinding body early in the turn. This makes sense with medium radius and longer radius turns.